Rainy Bus Stops

problem

AOR Ika is at the $S$ th bus stop at time $0$ and wants to go from there to the $G$ th bus stop. The number of bus stops $N$ and $M$ routes (*) connecting different bus stops are given. The bus stops are numbered $1, \ dots, and N$, respectively. Each route consists of $4$ values: origin $u$, destination $v$, departure time $t$, and travel time $c$. You can catch the bus if you are at the departure $u$ at the time $t$ and arrive at the destination $v$ at the time $t + c$. While not on the bus, AOR Ika gets wet in the rain. When heading to the $G$ th bus stop through the route that minimizes the time of getting wet in the rain, output the total time of getting wet in the rain from the time $0$ to the arrival at the $G$ th bus stop.

(*) In graph theory terms, a path is a sequence of vertices and edges, but please note that it is used here to mean edges.

input

Input is given from standard input in the following format.

$N \ M \ S \ G$ $u_1 \ v_1 \ t_1 \ c_1$ $\ vdots$ $u_M \ v_M \ t_M \ c_M$

output

Print the minimum amount of time you get wet in one line. Also, output a line break at the end.

Example

Input

2 2 1 2 1 2 10 100 1 2 5 500

Output

5

inputFormat

outputFormat

output the total time of getting wet in the rain from the time $0$ to the arrival at the $G$ th bus stop.

(*) In graph theory terms, a path is a sequence of vertices and edges, but please note that it is used here to mean edges.

input

Input is given from standard input in the following format.

$N \ M \ S \ G$ $u_1 \ v_1 \ t_1 \ c_1$ $\ vdots$ $u_M \ v_M \ t_M \ c_M$

output

Print the minimum amount of time you get wet in one line. Also, output a line break at the end.

Example

Input

2 2 1 2 1 2 10 100 1 2 5 500

Output

5

样例

2 2 1 2
1 2 10 100
1 2 5 500

5